I have to be able to understand your handwriting and do not skip any steps at all please. Please submit the entire filled out document by 12 pm tomorrow.

I have to be able to understand your handwriting and do not skip any steps at all please. Please submit the entire filled out document by 12 pm tomorrow.


One of life’s most painful moments comes when we must admit that we didn’t do our homework, that we are prepared. – Merlin Olsen MATH 322 HAND-IN HW 1 Prof. B. M. Patiak Name: Due: 1/25/2024 You must use the space provided for your work. You can use extra paper (must be computer paper) if the space provided is NOT enough. All work should be written in PENCIL only. Write legibly and avoid erasures. A. State the order of the given differential equation. Also, determine if the differential equation is linear or non-linear. If the is non-linear, state your reason briefly by identifying the non-linear term. B. Verify that the indicated function is an explicit solution of the given differential equation. 5. 2?′ = ?3 cos ? , ? = 1 √1 − sin ? One of life’s most painful moments comes when we must admit that we didn’t do our homework, that we are prepared. – Merlin Olsen B. Find the particular solution of the following IVP. Then identify the largest interval where the solution is valid. 6. ?′ + 2??2 = 0, ?(−2) = 1 2 ; ? = 1 ?2 + ? C. Find the particular solution of the following IVP. 7. ?′′ + ? = 0, ? ( ? 4 ) = √2, ?′ ( ? 4 ) = 2√2; ?(?) = ?1 cos(?) + ?2 sin(?) One of life’s most painful moments comes when we must admit that we didn’t do our homework, that we are prepared. – Merlin Olsen D. For the following differential equations, construct the slope field for [−3, 3] and sketch the solution curve at the indicated points. One of life’s most painful moments comes when we must admit that we didn’t do our homework, that we are prepared. – Merlin Olsen 10. Consider the autonomous differential equation ?? ?? = ?(? − 1)(? + 2) a) Identify all equilibria of the system. Equilibrium solutions are when ?? ?? = 0 b) Draw the direction field for this system on −3 ≤ ? ≤ 3 and ? > 0. Include sufficient amount of integral curves to give sense of the dynamics. c) Determine how the solutions behave as ? → ∞ and if this behavior depends on the value of ?(0). Describe this dependency. One of life’s most painful moments comes when we must admit that we didn’t do our homework, that we are prepared. – Merlin Olsen 11. Consider the first order autonomous equation: ?′ = ?(2 − ?)(? + 3)2 a) Find all equilibrium solutions. Draw the direction or slope fields. b) If ?(2) = −3, what is ?(60)? c) If ?(−6) = 0.3333, what is lim ?→∞ ?(?) =